"I think it will be late (Tuesday) or Wednesday," when the Senate votes on a possibly rewritten version of the House bill, said Sen. Jabo Wag­goner, R-Vestavia Hills. Waggoner is chairman of the Senate Rules Committee, which decides which bills go to the floor for debate.

"They are still talking and negotiating and tweaking and working on the bill," Waggoner said.

Beason said he and Hammon, legislative leaders and lawyers met for more than 11 hours last week discussing how much to change various sections of Alabama's law -- including the "reasonable suspicion" section that would allow police officers to question and detain suspected illegal immigrants.

"We went through every single section that I had adjusted, or the House had adjusted, and had a debate, lively debate at times," Beason said.

"It was a long, long process," Beason said.

Beason said he had not seen a draft of a new bill yet.

Hammon, who collaborated with Beason on the original 2011 law, said legislators still were having discussions, and the goal is to have a clear law that will be enforced.

"The bottom line is illegals are starting to come back to Alabama now," Hammon said.

Beason said one of the issues that was discussed was not changing sections of Alabama's 2011 law that are similar to an Arizona law now before the U.S. Supreme Court. The court is expected to rule on the constitutionality of that law this summer.

Senate President Pro Tempore Del Marsh, R-Anniston, also said he hopes to get the bill up for debate early this week.

"I believe Tuesday -- Wednesday at the latest -- we will be on the floor with the legislation," Marsh said.